C-浮点precision [英] C- Floating point precision

问题描述

我有一个程序，

int main()   
{   
        float f=0.0f;  
        int i;  

        for(i=0;i<10;i++) 
                f = f + 0.1f; 

        if(f == 1.0f) 
                printf("f is 1.0 \n"); 
        else 
                printf("f is NOT 1.0\n"); 

        return 0; 
} 

它总是打印f不是1.0。我理解，这是涉及到浮点precision在C.但我不知道它的确切位置是越来越混乱。有人可以请解释我为什么不打印的其他线路？

It always prints "f is NOT 1.0" . I understand this is related to floating point precision in C. But I am not sure exactly where it is getting messed up. Can someone please explain me why it is not printing the other line?

推荐答案

二进制浮点数不能重新present值0.1准确，因为它的二进制展开没有数字的有限数量（以完全相同的方式1/7的十进制扩展并非如此）。

Binary floating point cannot represent the value 0.1 exactly, because its binary expansion does not have a finite number of digits (in exactly the same way that the decimal expansion of 1/7 does not).

0.1二进制扩张

0.000110011001100110011001100...

当截断为IEEE-754单precision，这大约是十进制 0.100000001490116119 。这意味着，每一次将近0.1值添加到您的变量，你积累一个小错误 - 所以最终值略高于 1.0

When truncated to IEEE-754 single precision, this is approximately 0.100000001490116119 in decimal. This means that each time you add the "nearly 0.1" value to your variable, you accumulate a small error - so the final value is slightly higher than 1.0.

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